Shrinkage Estimation and Forecasting in Dynamic Regression Models Under Structural Instability

Abstract

Abstract This paper introduces a Stein-like shrinkage method for estimating slope coefficients and forecasting in first order dynamic regression models under structural breaks. The model allows for unit root and non-stationary regressors. The proposed shrinkage estimator is a weighted average of a restricted estimator that ignores the break in the slope coefficients, and an unrestricted estimator that uses the observations within each regime. The restricted estimator is the most efficient estimator but inconsistent when there is a break. However, the unrestricted estimator is consistent but not efficient. Therefore, the proposed shrinkage estimator balances the trade-off between the bias and variance efficiency of the restricted estimator. The averaging weight is proportional to the weighted distance of the restricted estimator, and the unrestricted estimator. We derive the analytical large-sample approximation of the bias, mean squared error, and risk for the shrinkage estimator, the unrestricted estimator, and the restricted estimator. We show that the risk of the shrinkage estimator is lower than the risk of the unrestricted estimator under any break size and break points. Moreover, we extend the results for the model with a unit root and non-stationary regressors. We evaluate the finite sample performance of our proposed method via extensive simulation study, and empirically in forecasting output growth.